Std 5 Mathematics · Chapter 10

10. Measuring Time

Solutions to Problem Sets 43 to 45, with clock diagrams — reading clocks, am/pm, the 24 hour clock and time calculations. Maharashtra State Board (Balbharati), Grade Five Mathematics, Part Two.

Key Ideas

Units: 1 minute = 60 seconds; 1 hour = 60 minutes; 1 day = 24 hours.

12 hour clock: times from 12 midnight to 12 noon are am; times from 12 noon to 12 midnight are pm.

24 hour clock: after 12 noon, keep counting 13, 14, … 23. For a pm time, add 12 to the hour: 5:40 pm = 17:40. Midnight is 00:00.

Adding time: add minutes, then hours. If the minutes are 60 or more, change 60 minutes into 1 hour.

Subtracting time: if the minutes above are fewer, borrow 1 hour = 60 minutes.

Problem Set 43

1Write the time shown in each clock in the box given below it.

2:25 — 25 minutes past 2 (minute hand on 5, hour hand between 2 and 3)
7:50 — 10 minutes to 8 (minute hand on 10, hour hand just before 8)
8:05 — 5 minutes past 8 (minute hand on 1, hour hand just after 8)
4:40 — 20 minutes to 5 (minute hand on 8, hour hand between 4 and 5)

The longer hand is the minute hand. Multiply the number it points to by 5 to get the minutes. The shorter hand shows the hour it has passed.

2Draw the hands of the clock to show the time given in the box.

Four thirty — 4:30

Quarter past nine — 9:15

Quarter to five — 4:45

20 minutes past 11 — 11:20

Four thirty: minute hand on 6; hour hand halfway between 4 and 5.
Quarter past nine: minute hand on 3; hour hand a little past 9.
Quarter to five: minute hand on 9; hour hand three-quarters of the way from 4 to 5.
20 minutes past 11: minute hand on 4; hour hand a third of the way from 11 to 12.

In the figures, the short thick hand is the hour hand and the long green hand is the minute hand.

3If a bus that leaves Nashik at 5 o’clock in the morning reaches Pune that same day at ten thirty in the morning, how long does the journey take?

Hr Min 10 30− 5 0 5 30

10:30 − 5:00 = 5 hours 30 minutes. The journey takes 5 hours 30 minutes (five and a half hours).

4A play that was to start at nine fifteen at night was delayed by half an hour because of a power outage. What time did the play start?

9:15 pm + 30 minutes = 9:45 pm. The play started at 9:45 pm (a quarter to ten at night).

5If a train leaves Mumbai at ten fifteen at night and reaches Nagpur at one forty the next afternoon, how long does the journey take?

10:15 pm to 12 midnight: 1 hour 45 minutes

12 midnight to 1:40 pm (13:40) next day: 13 hours 40 minutes

Total: 1 hr 45 min + 13 hr 40 min = 14 hr 85 min = 15 hours 25 minutes

The journey takes 15 hours 25 minutes.

Problem Set 44

1The time below is given by the 12 hour clock. Write the same by the 24 hour clock.

30 minutes past 10 in the morning = 10:30
10 minutes past 8 in the morning = 08:10
20 minutes past 1 in the afternoon = 1 + 12 = 13:20
40 minutes past 5 in the evening = 5 + 12 = 17:40

2Match the following.

12 hour clock	24 hour clock
9:10 am	9:10
2:10 pm	14:10
5:25 pm	17:25
11:10 pm	23:10
7:25 am	7:25

am times stay the same; for pm times add 12 to the hour.

Problem Set 45

1Add the following.

(1) Hr Min 2 30+ 4 55 6 85 7 25

(2) Hr Min 3 50+ 4 20 7 70 8 10

(3) Hr Min 3 45+ 1 35 4 80 5 20

(4) Hr Min 4 15+ 2 50 6 65 7 5

2 hours 30 minutes + 4 hours 55 minutes = 7 hours 25 minutes (85 min = 1 hr 25 min)
3 hours 50 minutes + 4 hours 20 minutes = 8 hours 10 minutes (70 min = 1 hr 10 min)
3 hours 45 minutes + 1 hour 35 minutes = 5 hours 20 minutes (80 min = 1 hr 20 min)
4 hours 15 minutes + 2 hours 50 minutes = 7 hours 5 minutes (65 min = 1 hr 5 min)

2Subtract the following.

(1) Hr Min 2 70 3 10− 2 40 0 30

(2) Hr Min 4 80 5 20− 2 35 2 45

(3) Hr Min 3 85 4 25− 1 55 2 30

(4) Hr Min 5 75 6 15− 2 45 3 30

3 hours 10 minutes − 2 hours 40 minutes = 30 minutes
5 hours 20 minutes − 2 hours 35 minutes = 2 hours 45 minutes
4 hours 25 minutes − 1 hour 55 minutes = 2 hours 30 minutes
6 hours 15 minutes − 2 hours 45 minutes = 3 hours 30 minutes

In every subtraction here the minutes above are fewer, so 1 hour is borrowed and changed into 60 minutes (shown in green on the top line).

3A government office opens at 7 in the morning and closes at 3 in the afternoon. How long is this office open?

3 in the afternoon = 15:00. 15:00 − 7:00 = 8 hours.

The office is open for 8 hours.

4A movie starts at 45 minutes past 3 in the afternoon and finishes two and a half hours later. At what time does the movie end?

Hr Min 3 45+ 2 30 5 75 6 15

3:45 + 2 hr 30 min = 5 hr 75 min = 6 hr 15 min. The movie ends at 6:15 pm (quarter past six in the evening).

5Sakharam was ploughing the field from 8 in the morning. At 12:30 in the afternoon he stopped and started for home. He reached home at 1:30. How long was he ploughing the field? How long did it take him to reach home from the field?

Ploughing: 8:00 am to 12:30 pm = 12:30 − 8:00 = 4 hours 30 minutes
Going home: 12:30 pm to 1:30 pm = 1 hour

6Rambhau started the water pump at ten thirty at night and put it off the same night at a quarter to twelve. How long was the water pump on?

Hr Min 11 45− 10 30 1 15

11:45 pm − 10:30 pm = 1 hour 15 minutes. The pump was on for 1 hour 15 minutes.

7Geeta taught in the classroom for 2 hours and 25 minutes in the morning and 1 hour and 45 minutes in the afternoon. How long was she teaching in all?

Hr Min 2 25+ 1 45 3 70 4 10

2 hr 25 min + 1 hr 45 min = 3 hr 70 min = 4 hr 10 min. She taught for 4 hours 10 minutes in all.

8If a bank is open for business from 10 in the morning to 4:30 in the evening, how long is it open?

Hr Min 16 30− 10 0 6 30

4:30 in the evening = 16:30. 16:30 − 10:00 = 6 hours 30 minutes. The bank is open for 6 hours 30 minutes.

9If a shop is open from 9:30 am to 10 pm, how long is it open?

Hr Min 21 60 22 0− 9 30 12 30

10 pm = 22:00. 22:00 − 9:30 = 12 hours 30 minutes. The shop is open for 12 hours 30 minutes.

10If the Maharashtra Express leaving from Kolhapur at 15:30 arrives at Gondia the next day at 20:15, how long is the journey from Kolhapur to Gondia?

15:30 to 24:00 (midnight): 24:00 − 15:30 = 8 hours 30 minutes

00:00 to 20:15 next day: 20 hours 15 minutes

Total: 8 hr 30 min + 20 hr 15 min = 28 hours 45 minutes

The journey takes 28 hours 45 minutes, that is, 1 day 4 hours 45 minutes.

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